Why do we square the weights in the Herfindahl index?

by Ad Min - If you donâ€™t square the market shares (weights) and simply sum them up , you will only get back unity as the sum of the weights is one by construction!

The choice of squaring the weights, instead of e.g., raising to the third power is essentially arbitrary. In fact there are generalizations going under the name Hannah-Kay indexes where you can choose which power to use.

The choice of squaring the weights, instead of e.g., raising to the third power is essentially arbitrary. In fact there are generalizations going under the name Hannah-Kay indexes where you can choose which power to use.